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As Black Scholes model, you can assume a two-sided Truncated Normal Distribution as riskneutral density $f(x)$ (with $\mu=0,\sigma=T-t$) for the returns and then price the option payoff $H$ as usual b …

The fact that you can solve the second set of equations means that you can hedge the option through another asset aswell, in a simple binomial world this may indeed be true. Note that your strategy mu …

The next throw is independent of the previous throws, so you only calculate the value of the future expected payoffs from the option to continue. How many "$n$"s does the dice have, and what is their …

Its a stylized fact in academia that put options are overpriced. E.g., the monthly average return on S&P500 put options is around -40% for ATM options. The most often quoted reason for this phenomen …

It is not possible to derive the joint distribution from the expectation under the given information here. The fact that you have the expectation for all $K$ says nothing about the joint distribution …

The No-Arbitrage bounds for a European put are: $$ (Ke^{-rT}-S)^+ \leq P \leq K e^{-rT}$$ This is because the maximum payoff at maturity is $K$ (discounted) and the minimum value is the discounted i …

These options can be priced by adding an early exercise premium value to the intrinsic value: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.542.3141&rep=rep1&type=pdf

What is the formula for the vanilla option (Call/Put) price in the Heston model? I only found the bi-variate system of stochastic differential equations of Heston model but no expression for the opt …

You can always estimate the expectation by simulating the distribution. In your case if it is a European option, you can just calculate the average simulated payoff. If it is an American option you ca …

In the past, most literature assumed a risk-averse investor to model utility preferences. This includes the CRRA and CARA utility functions. In recent papers, researchers state that investors may be …

No you need to subtract the cost of entering your position as well as the financing costs thereof. In this case you actually receive net \$1 option premiums which yields additional interest at maturit …

What are the upper and lower bound of American call and put options for an underlying with continuous dividend yield? For European options, the bounds are known as \begin{align*} [S_te^{-d\tau}-Ke^{ …

In general, if one can create a portfolio with the same payoff as the derivative, their prices must be equal. This is also called "Law of One Price". Here an excerpt from my script: Here EMM = Equiv …

The condition $$ud=1\text{, or equivalently }u=1/d$$ is necessary to ensure convergence of the Binomial tree's mean $\mu$ and standard deviation $\sigma$ to nonfinite values when $n$ (number of step …

You can use the "Merton Jump Diffusion Model" to price European Options with jumps. The other points of your question are rather of practical relevance only. The negative drift of the underlying is u …